Information Closure Method for Dynamic Analysis of Nonlinear Stochastic Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 353-363 ◽  
Author(s):  
R. J. Chang ◽  
S. J. Lin
Keyword(s):  
Stochastic Systems ◽  
Analytical Investigation ◽  
Stochastic Dynamic ◽  
Moment Equations ◽  
Nonlinear Stochastic Systems ◽  
Explicit Analysis ◽  
The Moment ◽  
Stochastic Dynamic Systems ◽  
Closure Method ◽  
Independent Mode

An information closure method for analytical investigation of response statistics and robust stability of nonlinear stochastic dynamic systems is proposed. Entropy modes are defined first based on the decomposition of probability density functions estimated by maximizing entropy in quasi-stationary. Then the entropy modes are selected and employed in the moment equations as the constraints for information closure. The estimated density with Lagrange multipliers is used for the closure of the hierarchical moment equations. By selecting single independent mode in every state, an explicit analysis of the entropy and density function can be obtained. The performance of the closure method is supported by employing three stochastic systems with some stationary exact solutions and through Monte Carlo simulations.

scholarly journals Identification and Stochastic Optimizing the UAV Motion Control in Turbulent Atmosphere

2021 ◽  
Vol vm02 (is02) ◽  
pp. 57-63
Author(s):  
Yevgeny Somov ◽  
Nikolay Rodnishchev ◽  
Tatyana Somova
Keyword(s):  
Stochastic Systems ◽  
Time Moment ◽  
Translational Motion ◽  
Stochastic Dynamic ◽  
Random Parameters ◽  
Nonlinear Stochastic Systems ◽  
Control Functions ◽  
Angular Velocities ◽  
Aerial Vehicle ◽  
Stochastic Dynamic Systems

In a class of diffusion Markov processes, we formulate a problem of identification of nonlinear stochastic dynamic systems with random parameters, multiplicative and additive noises, control functions, and the state vector at a final time moment. For such systems, the identifiability conditions are being studied, and necessary conditions are formulated in terms of the general theory of extreme problems. The developed engineering methods for identification and optimizing nonlinear stochastic systems are presented as well as their application for unmanned aerial vehicles under wind disturbances caused by atmospheric turbulence, namely, for optimizing the autopilot parameters during a rotary maneuver of an unmanned aerial vehicle in translational motion, taking into account the identification of its angular velocities.

Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory

2005 ◽  
Vol 58 (3) ◽  
pp. 178-205 ◽  
Author(s):  
L. Socha
Keyword(s):  
Dynamic Systems ◽  
Stochastic Systems ◽  
Stochastic Dynamic ◽  
Density Functions ◽  
Mathematical Tool ◽  
Nonlinear Stochastic Systems ◽  
Theoretical Approaches ◽  
Linearization Methods ◽  
Stochastic Dynamic Systems ◽  
Linearization Techniques

The purpose of Part 1 of this paper is to provide a review of recent results from 1991 through 2003 in the area of theoretical aspects of statistical and equivalent linearization in the analysis of structural and mechanical nonlinear stochastic dynamic systems. First, a discussion about misunderstandings appearing in the literature in derivation of linearization coefficients for mean-square linearization criterion is presented. In Secs. 3–6 new theoretical results, including new types of criteria, nonlinearities, and excitations in the context of linearization methods, are reviewed. In particular, moment criteria called energy criteria, linearization criteria in the space of power spectral density functions and probability density functions are discussed. A survey of a wide class of so-called nonlinearization techniques, including equivalent quadratization and equivalent cubicization methods, is given in Sec. 7. New linearization techniques for nonlinear stochastic systems with parametric Gaussian excitations and external non-Gaussian excitations are discussed in Secs. 8 and 9, respectively. In the last sections, four surveys of papers where stochastic linearization is used as a mathematical tool in other theoretical approaches, namely, models of dynamic systems with hysteresis, finite element method, and control of nonlinear stochastic systems and linearization with sensitivity analysis, are given. A discussion of the accuracy analysis of linearization techniques and some general conclusions close this paper. There are 217 references cited in this revised article.

Linearization in Analysis of Nonlinear Stochastic Systems, Recent Results—Part II: Applications

2005 ◽  
Vol 58 (5) ◽  
pp. 303-315 ◽  
Author(s):  
L. Socha
Keyword(s):  
Stochastic Systems ◽  
Squeeze Film ◽  
Equivalent Linearization ◽  
Stochastic Dynamic ◽  
Offshore Platforms ◽  
Wood Structures ◽  
Stochastic Excitations ◽  
Runoff Modeling ◽  
Traditional Fields ◽  
Stochastic Dynamic Systems

The purpose of this part of the paper is to provide a review of recent results (1991–2003) in the applications of statistical and equivalent linearization in the analysis of structure and mechanical nonlinear stochastic dynamic systems. Both the applications in “traditional fields” of engineering and a few examples from new fields are reported. Traditional fields include vibration of construction elements, such as beams, frames, shells, and plates, and also vibration of complex structures under earthquake or wind or wave stochastic excitations, or a combination of earthquake and wind or wind and wave excitations. Typical constructions are multistory structures, offshore platforms, and vehicle models. In the paper several examples from new fields, such as vibration of wood structures, block rocking, rainfall-runoff modeling, a squeeze film model, and an astronomy model are reviewed. A discussion of typical advantages and faults of linearization techniques and some general conclusions close the paper. There are 121 references cited in this review article.

The accurate continuous-discrete extended Kalman filter for continuous-time stochastic systems

2015 ◽  
Vol 30 (4) ◽  
Author(s):  
Gennady Yu. Kulikov ◽  
Maria V. Kulikova
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Stochastic Systems ◽  
Total Error ◽  
Stochastic Dynamic ◽  
Extended Kalman Filtering ◽  
New Approach ◽  
Error Covariance ◽  
The Moment

AbstractThis paper elaborates a new approach to nonlinear filtering based on an accurate implementation of the continuous-discrete extended Kalman filter. It implies that the moment differential equations for calculating the predicted state mean of stochastic dynamic system and the corresponding error covariance matrix are solved accurately, i.e. with negligible error. The latter allows the total error of the extended Kalman filter to be reduced significantly and results in a new Accurate Continuous-Discrete Extended Kalman Filtering method. The developed technique is compared theoretically and numerically with other implementations of the extended Kalman filter to conform its outstanding performance on test examples.

Feedback Control of Stochastic Systems to Track Prespecified Probability Density Functions

2005 ◽  
Author(s):  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Probability Density ◽  
Stochastic Systems ◽  
Control Design ◽  
Probability Density Functions ◽  
Density Functions ◽  
Moment Equations ◽  
Feedback Controls ◽  
The Moment ◽  
Non Gaussian ◽  
Probability Density Function Pdf

We present a study of feedback controls of stochastic systems to track a prespecified probability density function (PDF). The moment equations of the response are used in the control design to illustrate the underlining issues. A hierarchical approach is proposed to design the control for tracking Gaussian and non-Gaussian PDFs. The control design approach is demonstrated with a simple example.

scholarly journals Modeling of applied problems by stochastic systems and their analysis using the moment equations

2013 ◽  
Vol 2013 (1) ◽  
pp. 152 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Mária Michalková ◽  
Miroslava Růžičková
Keyword(s):  
Stochastic Systems ◽  
Moment Equations ◽  
The Moment

The continuous–discrete extended Kalman filter revisited

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gennady Yu. Kulikov ◽  
Maria V. Kulikova
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Total Error ◽  
Waiting Times ◽  
Stochastic Dynamic ◽  
Extended Kalman Filtering ◽  
Gaussian Density ◽  
The Moment ◽  
Stochastic Dynamic Systems

AbstractThis paper elaborates a new approach to nonlinear filtering grounded in an accurate implementation of the continuous–discrete extended Kalman filter for estimating stochastic dynamic systems. It implies that the moment differential equations for calculation of the predicted state mean and error covariance of propagated Gaussian density are solved accurately, i.e., with negligible errors. The latter allows the total error of the extended Kalman filter to be reduced significantly and results in a new accurate continuous–discrete extended Kalman filtering method. In addition, this filter exploits the scaled local and global error controls to avoid any comparison of different physical units. The designed state estimator is compared numerically with continuous–discrete unscented and cubature Kalman filters to expose its practical efficiency. The problem of long waiting times (i.e., infrequent measurements) arisen in chemical and other engineering is also addressed.

Application of Wavelets in Modeling Stochastic Dynamic Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 763-769 ◽  
Author(s):  
O. P. Agrawal
Keyword(s):  
Dynamic Systems ◽  
Stochastic Systems ◽  
Random Coefficients ◽  
The State ◽  
Stochastic Dynamic ◽  
State Variables ◽  
Algebraic Equations ◽  
Random Forcing ◽  
Forcing Function ◽  
Stochastic Dynamic Systems

This paper presents a wavelet based model for stochastic dynamic systems. In this model, the state variables and their variations are approximated using truncated linear sums of orthogonal polynomials, and a modified Hamilton’s law of varying action is used to reduce the integral equations representing dynamics of the system to a set of algebraic equations. For deterministic systems, the coefficients of the polynomials are constant, but for stochastic systems, the coefficients are random variables. The external forcing functions are treated as stationary Gaussian processes with specified mean and correlation functions. Using Karhunen-Loeve (K-L) expansion, the random input processes are represented in terms of linear sums of finite number of orthonormal eigenfunctions with uncorrelated random coefficients. A wavelet based technique is used to solve the integral eigenvalue problem. Application of wavelets and K-L expansion reduces the infinite dimensional input force vector to one with finite dimensions. Orthogonal properties of the polynomials and the wavelets are utilized to make the algebraic equations sparse and computationally efficient. A method to compute the mean and the variance functions for the state processes is developed. A single degree of freedom spring-mass-damper system subjected to a random forcing function is considered to show the feasibility and effectiveness of the formulation. Studies show that the results of this formulation agree well with those obtained using other schemes.

Sign in / Sign up

Export Citation Format

Share Document